This RMD will look in some detail at the items that have had unusually high price changes in the pandemic.
The following code (not shown in markdown) will import and format the BEA data from csv tables. All of this is duplicated from Wavelet Analysis of Variance v2.
The following function (not shown in markdown) allows querying the main tables (exp, qua, and pri) based on item levels, where goods and services are level 1; durable goods, nondurable goods, and HH cons exp on services are level 2; and so on. Often, we’ll want the lowest (i.e. most granular level), which can be retrieved with the lowestLevel = T parameter. This is the same as in Process PCE Data.Rmd
This will build the itemClass table that’s the same in Wavelet Analysis of Variance v2.RMD.
## Item Pan.Price.Pct.Chg
## 97 Less: Personal remittances in kind to nonresidents 13.99532
## 51 Fish and seafood 14.47634
## 154 Pension funds 14.47958
## 191 Domestic services 15.03469
## 9 Tires 15.27404
## 50 Poultry 15.92873
## 11 Furniture 17.67825
## 48 Pork 19.37330
## 54 Eggs 20.21869
## 47 Beef and veal 23.39831
## 15 Major household appliances 24.32774
## 66 Food produced and consumed on farms (6) 24.98299
## 73 Gasoline and other motor fuel 30.06328
## 107 Natural gas (28) 30.07890
## 76 Other fuels 30.58331
## 75 Fuel oil 32.74359
## 6 Employee reimbursement 33.14583
## 118 Motor vehicle rental 33.14643
## 4 Net transactions in used autos 54.63929
## 7 Net transactions in used trucks 54.63959
## 8 Used truck margin 85.93548
## 5 Used auto margin 85.93752
## NA <NA> NA
## NA.1 <NA> NA
## NA.2 <NA> NA
## NA.3 <NA> NA
## NA.4 <NA> NA
## NA.5 <NA> NA
## NA.6 <NA> NA
## NA.7 <NA> NA
## NA.8 <NA> NA
## NA.9 <NA> NA
## NA.10 <NA> NA
## NA.11 <NA> NA
## NA.12 <NA> NA
## NA.13 <NA> NA
## NA.14 <NA> NA
## NA.15 <NA> NA
As a first pass, I want to grab only those items whose pandemic average monthly percentage price change was 0.5 above the average in the decade prior to the pandemic. Here they are, including the wavelet correlation (P & Q) for the first detail (2-4 months).
| Item | Pan.Avg.Chg | Pre.Pan.Avg.Chg | d1Cor | |
|---|---|---|---|---|
| 179 | Televisions | 0.04487 | -1.507 | -0.3643 |
| 138 | Personal computers/tablets and peripheral equipment | 0.2197 | -0.6021 | -0.4598 |
| 142 | Photographic equipment | 0.3856 | -0.3316 | -0.2799 |
| 172 | Sporting equipment, supplies, guns, and ammunition (part of 80) | 0.4298 | -0.2012 | -0.3276 |
| 18 | Clocks, lamps, lighting fixtures, and other household decorative items | 0.4051 | -0.4838 | -0.4975 |
| 129 | Outdoor equipment and supplies | 0.5225 | -0.02897 | -0.3085 |
| 109 | New domestic autos | 0.5536 | 0.02167 | -0.1925 |
| 110 | New foreign autos | 0.5536 | 0.02167 | -0.1353 |
| 183 | Tires | 0.6081 | 0.02536 | -0.2418 |
| 147 | Poultry | 0.6443 | 0.1174 | -0.5309 |
| 56 | Furniture | 0.7242 | -0.0658 | -0.1541 |
| 146 | Pork | 0.7978 | 0.1631 | -0.487 |
| 32 | Eggs | 0.7775 | 0.1276 | -0.9262 |
| 8 | Beef and veal | 0.9378 | 0.3452 | -0.4467 |
| 89 | Major household appliances | 1.082 | -0.1734 | -0.2658 |
| 46 | Food produced and consumed on farms (6) | 0.7018 | 0.184 | -0.9843 |
| 59 | Gasoline and other motor fuel | 1.111 | 0.08246 | 0 |
| 105 | Natural gas (28) | 1.081 | -0.09427 | -0.2258 |
| 120 | Other fuels | 1.156 | 0.02632 | -0.271 |
| 54 | Fuel oil | 1.092 | 0.08646 | -0.4041 |
| 37 | Employee reimbursement | 1.462 | 0.07295 | -0.7016 |
| 100 | Motor vehicle rental | 1.462 | 0.07295 | -0.1651 |
| 107 | Net transactions in used autos | 1.878 | -0.0265 | 0 |
| 108 | Net transactions in used trucks | 1.878 | -0.0265 | 0 |
| 190 | Used truck margin | 2.933 | -0.1866 | 0 |
| 189 | Used auto margin | 2.933 | -0.1866 | 0 |
Whether using discrete or continuous wavelet transforms, wavelet analysis is, in essence, a way to characterize the “spectral characteristics of a time-series as a function of time, revealing how the different periodic components of a particular time-series evolve over time,” (Aguiar-Conraria and Soares 2011, 478). Whereas Fourier transforms show the frequency distribution of a whole series, wavelets can locate power at various frequencies for particular times in the series. This is done by projecting a wavelet at different scales, s, (widths) and translations, \(\tau\) (time locations) onto the series, \(x_t\). Hence, the continuous wavelet transform with respect to a chosen wavelet function \(\psi\) can be expressed as:
\[W_x(\tau, s) = \int x_t \left[\frac{1}{\sqrt{|s|}}\bar\psi \left(\frac{t-\tau}{s} \right) \right]\]
with the bar denoting complex conjugation (Auigar-Conraria and Soares 2011, 479). As we will ultimately be looking at synchronism between price and quantity for our Personal Consumption Expenditure items, an analytic wavelet is appropriate. As Aquiar-Conraria and Soares (2011, 479) note, “Analytic wavelets are ideal for the analysis of oscillatory signals, since the continuous analytic wavelet transform provides an estimate of the instantaneous amplitude and instantaneous phase of the signal in the vicinity of each time/scale location (\(\tau\), s).” Following those same authors, we utilize the Morlet wavelet, given by
\[\psi_{\omega_0}(t) = \pi^{-1/4}e^{i\omega_0t}e^{-\frac{t^2}{2}}\]
See Aquiar-Conraria and Soares (2011, 479) for the advantages of using this wavelet.
Once the wavelet is chosen, it is possible to calculate wavelet power spectra showing the distribution of variance in terms of both scale (frequency) and time. Furthermore, wavelet coherency between two time-series can be calculated (see Aguiar-Conraria and Soares 2011, 49-80 for more information).
(Note: the authors develop a system for comparing ‘distance’ between two wavelet spectra which they’ll use for cluster analysis. We might want to try this at some point, though it would be essentially similar, I think, to the DWT stuff we did. A good check at the least, but possibly just a superior approach.)
[Wavecomp looks like a significant extension of the Aguiar… stuff. Lots of good examples in its documentation]
Here are the Continuous Wavelet Transform plots for those items.